Certain embodiments described herein are generally related to digital imaging, and more specifically, to standard and Fourier ptychographic imaging systems and methods with convex relaxation.
Ptychography imaging involves collecting lower resolution images and then reconstructing the image data to form a higher resolution image. Over the past two decades, ptychographic imaging has been used in a variety of regimes to produce high-resolution, wide field-of-view images of microscopic and nanoscopic phenomena. Whether in the X-ray regime at third-generation synchrotron sources, in the electron microscope for atomic scale phenomena, or in the in the optical regime for biological specimens, ptychography has shown an unparalleled ability to acquire hundreds of megapixels of sample information near the diffraction limit. Typically, the underlying operation of ptychography is to sample a series of diffraction patterns from a specimen as it is scanned through a focused beam. These intensity-only measurements are then reconstructed into a complex (i.e. amplitude and phase), high-resolution image with more pixels of sample information than any single recorded diffraction pattern.
Most recently, a Fourier ptychographic microscope (FPM) was introduced that uses a Fourier ptychographic technique that can reconstruct gigapixel optical images from a sequence of lower resolution images collected using a low NA objective lens from a conventional microscope. In one example, Fourier ptychographic microscope activates different LEDs in an LED array to illuminate a sample from different directions while the low-resolution images are captured. As in standard ptychography, Fourier ptychography recovers the sample's phase as it merges together the captured image sequence into a high-resolution output.
Conventional ptychographic imaging systems can avoid the need for a high NA, well-corrected objective lens to image at the diffraction-limit by resolving resolution-limiting factors in their data capture and reconstruction techniques. However, these systems lack stable, robust, and accurate reconstruction methods. For example, conventional ptychographic systems reconstruct the phase of the scattered field from measured intensities using non-convex algorithms. Most of these conventional systems solve the phase retrieval problem by applying known constraints in an iterative manner using an “alternating projection” (AP) strategy. Reconstruction techniques that use AP strategies tend to converge to incorrect local minima and/or to stagnate.